TeV-scale seesaw mechanism with quintuplet fermions

Kresimir Kumericki, Ivica Picek, and Branimir Radovcic

Department of Physics, Faculty of Science, University of Zagreb, P.O.B. 331, HR-10002 Zagreb, Croatia(Received 4 May 2012; published 6 July 2012)

We propose a new seesaw model based on a fermionic hypercharge-zero weak quintuplet in conjunction

with an additional scalar quadruplet which attains an induced vacuum expectation value. The model

provides both tree-level seesaw �v6=M5 and loop-suppressed radiative �ð1=16�2Þ � v2=M contributions

to active neutrino masses. The empirical masses m� � 10�1 eV can be achieved with M� TeV new

states, accessible at the LHC. For 5 fb�1 of accumulated integrated luminosity at the LHC, there could be

�500 doubly-charged �þþ or �þþ fermions with mass M� ¼ 400 GeV, leading to interesting multi-

lepton signatures. The neutral component of the fermion quintuplet, previously identified as a minimal

dark matter candidate, becomes unstable in the proposed seesaw setup. The stability can be restored by

introducing a Z2 symmetry, in which case neutrinos get mass only from radiative contributions.

DOI: 10.1103/PhysRevD.86.013006 PACS numbers: 14.60.Pq, 14.60.St, 95.35.+d

I. INTRODUCTION

We propose a seesaw model built upon the hypercharge-zero fermionic weak quintuplet which, in isolation,provides a viable dark matter (DM) particle within theso-called minimal dark matter (MDM) model [1]. Weexplore the conditions under which the quintuplets �R �ð1; 5; 0Þ could simultaneously generate the masses of theknown neutrinos and provide a stable DM candidate.

The proposed model goes beyond the three tree-levelrealizations of Weinberg’s effective dimension-five opera-tor LLHH [2]: type I [3], type II [4], and type III [5]seesaw mechanisms, mediated by a heavy fermion singlet,a scalar triplet, and a fermion triplet, respectively. A see-saw mediator of isospin larger than one has to be accom-panied by a scalar multiplet larger than that of the standardmodel (SM) Higgs doublet.

Our previous model [6,7], based on an exotic nonzerohypercharge weak quintuplet Dirac fermion �R � ð1; 5; 2Þ,generates the neutrino masses both at the tree level andat the loop level. At the tree level it corresponds todimension-nine seesaw operator which reproduces the em-pirical neutrino masses m� � 10�1 eV with M� � few100 GeV states testable at the LHC, while for heaviermasses, which are outside of the LHC reach, these exoticleptons generate radiative neutrino masses. However, ifone expects from new states to accomplish simultaneouslythe DM mission, they should have zero hypercharge.

A recent ‘‘R�MDM model’’ [8] of purely radiativeneutrino (R�) masses employs hypercharge-zero quintu-plets �R � ð1; 5; 0Þ which, taken in isolation, provide aviable MDM candidate [1]. In a separate paper [9] weidentify an omitted term in [8] which spoils the claimedDM stability. Therefore, we adopt here a more generalapproach in which we analyze in detail both the tree-level and the radiative neutrino masses generated byhypercharge-zero quintuplets �R � ð1; 5; 0Þ. Thereby weaddress also the phenomenology of these states at the LHC

and recall that by imposing a Z2 symmetry, one can rec-oncile the seesaw mission with the viability as a DM.

II. THE MODELWITH FERMIONICQUINTUPLETS

As announced above, the model we propose here isbased on the symmetry of the SM gauge group SUð3ÞC �SUð2ÞL �Uð1ÞY . In addition to usual SM fermions, weintroduce three generations of hypercharge-zero quintu-plets �R ¼ ð�þþ

R ;�þR ;�

0R;�

�R ;�

��R Þ, transforming as

(1, 5, 0) under the gauge group. Also, in addition to theSM Higgs doublet H ¼ ðHþ; H0Þ there is a scalar quadru-plet � ¼ ð�þ;�0;��;���Þ transforming as ð1; 4;�1Þ.This is in contrast to a recent model for radiative neu-

trino masses [8] adopted subsequently in [10], where a useof the scalar sextuplet �� ð1; 6;�1Þ avoids the tree-levelcontribution. In a tensor notation suitable to cope withhigher SUð2ÞL multiplets [8] our additional fields are to-tally symmetric tensors �Rijkl and �ijk with the following

components:

�R1111 ¼ �þþR ; �R1112 ¼ 1ffiffiffi

4p �þ

R ;

�R1122 ¼ 1ffiffiffi6

p �0R; �R1222 ¼ 1ffiffiffi

4p ��

R ;

�R2222 ¼ ���R ;

(1)

�111 ¼ �þ; �112 ¼ 1ffiffiffi3

p �0;

�122 ¼ 1ffiffiffi3

p ��; �222 ¼ ���:(2)

The gauge-invariant and renormalizable Lagrangian in-volving these new fields reads

PHYSICAL REVIEW D 86, 013006 (2012)

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L ¼ �Ri��D��R þ ðD��ÞyðD��Þ

��LLY��R þ 1

2ð�RÞCM�R þ H:c:

�� VðH;�Þ:

(3)

Here, D� is the gauge-covariant derivative, Y is the

Yukawa-coupling matrix, and M is the mass matrix ofthe heavy leptons, which we choose to be real and diago-nal. For simplicity, we drop the flavor indices altogether.

The scalar potential has the gauge-invariant form

VðH;�Þ ¼ ��2HH

yH þ�2��

y�þ �1ðHyHÞ2þ �2H

yH�y�þ �3H�H���

þ ð�4H�HH�þ H:c:Þ þ ð�5HH��þ H:c:Þ

þ ð�6H����þ H:c:Þ þ �7ð�y�Þ2þ �8�

�����: (4)

In the adopted tensor notation the terms in Eqs. (3) and (4)read

LL��R ¼ LLi�jkl�Rij0k0l0�

jj0�kk0�ll

0;

ð�RÞC�R ¼ ð�RÞCijkl�Ri0j0k0l0�ii0�jj

0�kk

0�ll

0;

H�H��� ¼ H�iHj��jkl�ikl;

H�HH� ¼ H�iHjHk�ij0k0�jj0�kk

0;

HH�� ¼ Hi�jklHi0�j0k0l0�ij�i

0j0�kk0�ll

0;

H���� ¼ Hi��ijk�jlm�kl0m0�ll

0�mm0

;

������ ¼ ��ijk�i0jk��i0j0k0�ij0k0 :

(5)

Accordingly, the Majorana mass term for the quintuplet�R

is expanded in component fields to give

ð�RÞCM�R ¼ ð�þþR ÞCM���

R � ð�þR ÞCM��

R

þ ð�0RÞCM�0

R � ð��R ÞCM�þ

R

þ ð���R ÞCM�þþ

R ; (6)

the terms containing two charged Dirac fermions and oneneutral Majorana fermion

�þþ ¼ �þþR þ���C

R ; �þ ¼ �þR � ��C

R ;

�0 ¼ �0R þ�0C

R :(7)

The electroweak symmetry breaking proceeds in the usualway from the vacuum expectation value (VEV) v of theHiggs doublet, corresponding to the negative sign in frontof the �2

H term in Eq. (4). On the other hand, the electro-weak � parameter dictates a small value for the VEV v�ofthe scalar quadruplet, implying the positive sign in frontof the �2

� term. However, the presence of the �4 term in

Eq. (4), given explicitly by

H�HH�¼ 1ffiffiffi3

p Hþ�HþHþ��� 2ffiffiffi3

p H0�HþH0��

þH0�HþHþ���þHþ�H0H0�þ

� 2ffiffiffi3

p Hþ�HþH0�0þ 1ffiffiffi3

p H0�H0H0�0; (8)

leads to the induced VEV for the �0 field,

v� ’ � 1ffiffiffi3

p ��4

v3

�2�

: (9)

Since it changes the electroweak � parameter from theunit value to � ’ 1þ 6v2

�=v2, a comparison to the experi-

mental value � ¼ 1:0008þ0:0017�0:0007 [11] gives us a constraint

v� & 3:6 GeV.

III. NEUTRINO MASSES

The Yukawa interaction terms from Eq. (3), when ex-pressed like that in Eq. (5), read explicitly as

LL��R ¼ �ffiffiffi3

p2

��L���þ

R � 1ffiffiffi2

p �lL���0

R þffiffiffi3

p2

�lL�0��

R

þ 1ffiffiffi2

p ��L�0�0

R � 1

2��L�

þ��R � �lL�

þ���R

þ 1

2�lL�

���þR þ ��L�

���þþR : (10)

The VEV v� generates a Dirac mass term connecting �L

and �0R, a nondiagonal entry in the mass matrix for neutral

leptons given by

L��0 ¼�1

2ð ��Lð�0

RÞCÞ0 1ffiffi

2p Yv�

1ffiffi2

p YTv� M

0@

1A ð�LÞc

�0R

!þH:c:

(11)

A similar term connecting light and heavy charged leptonsgives the mass matrix for charged leptons

Ll�� ¼ �ðlL ð�þR ÞCÞ Ylv �

ffiffi3

p2 Yv�

0 M

!lR

ð�þL ÞC

!þ H:c:

(12)

After diagonalizing the mass matrix for the neutral leptons,the light neutrinos acquire the Majorana mass matrixgiven by

mtree� ¼ � 1

2v2�YM

�1YT: (13)

In the basis where the matrix of heavy leptons is real anddiagonal, M ¼ diagðM1;M2;M3Þ, we can write mtree

� as

ðm�Þtreeij ¼ � 1

2v2�

Xk

YikYjk

Mk

: (14)

Together with the induced VEV in Eq. (9), this gives

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ðm�Þtreeij ¼ � 1

6ð��

4Þ2v6

�4�

Xk

YikYjk

Mk

; (15)

which reflects the fact that the light neutrino mass isgenerated from the dimension-nine operator correspondingto the tree-level seesaw mechanism displayed on Fig. 1.

Besides at the tree level, the light neutrino masses arisealso through one-loop diagrams displayed on Fig. 2. Thecrucial quartic �5 term in Eq. (4), which, expanded incomponent fields gives

HH�� ¼ 2ffiffiffi3

p ���þH0H0 � 2

3����HþHþ

þ 2ffiffiffi3

p ����0HþHþ � 2

3�0�0H0H0

þ 2

3���0HþH0 � 2�þ���HþH0: (16)

There are two different contributions on Fig. 2, one withheavy neutral fields (�0, �0) and the other with heavycharged fields (�þ, �þ, ��) running in the loop. If weneglect the mass splitting within the � and � multiplets,the contribution to the light neutrino mass matrix isgiven by

ðm�Þloopij ¼ �5��5v

2

24�2

Xk

YikYjkMk

m2� �M2

k

�1� M2

k

m2� �M2

k

lnm2

�

M2k

�:

(17)

This expression can be further specified [12], depending onrelative values of the masses for additional fermion andscalar multiplets. For heavy fermions significantly heavierthan the new scalars, M2

k � m2�,

ðm�Þloopij ¼ �5��5v

2

24�2

Xk

YikYjk

Mk

�lnM2

k

m2�

� 1

�: (18)

In the opposite case, for m2� � M2

k ,

ðm�Þloopij ¼ �5��5v

2

24�2m2�

Xk

YikYjkMk: (19)

Finally, if m2� ’ M2

k , then

ðm�Þloopij ¼ �5��5v

2

48�2

Xk

YikYjk

Mk

: (20)

The tree-level and the loop contributions added togethergive the light neutrino mass matrix

ðm�Þij ¼ ðm�Þtreeij þ ðm�Þloopij

¼ �1

6ð��

4Þ2v6

�4�

Xk

YikYjk

Mk

þ�5��5v

2

24�2

Xk

YikYjkMk

m2� �M2

k

��1� M2

k

m2� �M2

k

lnm2

�

M2k

�: (21)

In the case of comparable masses the light neutrino massmatrix reads

ðm�Þij ¼��1

6ð��

4Þ2v6

�4�

þ�5��5v

2

48�2

�Xk

YikYjk

Mk

: (22)

From this expression we can estimate the high-energy scaleof our model and the corresponding value for v� in Eq. (9).For illustrative purposes, we take the same values for themass parameters (�� ¼ M� ¼ �NP) and the empiricalinput values v ¼ 174 GeV andm� � 0:1 eV. For the mod-erate values Y � 10�3, �4 � 10�2 and �5 � 10�4 we get

ν Σ ν

Φ Φ

FIG. 1. Tree-level diagram corresponding to dimension-nineoperator in Eq. (15). The fermion line flow indicates a Majorananature of the seesaw mediator.

ν Σ ν

Φ Φ

FIG. 2. One-loop diagrams generating the light neutrinomasses.

FIG. 3 (color online). For the portion of the parameter spaceleft from the equality-division line, where the tree-level contri-bution to neutrino masses dominates, we plot mtree=mloop. Right

from the equality-division line, the one-loop contribution toneutrino masses dominates, and we plot mloop=mtree.

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�NP ’ 440 GeV and v� ’ 160 MeV. Correspondingmasses of the new states could be tested at the LHC. InFig. 3 we display the part of the parameter space for whichthe tree-level (loop-level) contribution dominates.

IV. PRODUCTION OF QUINTUPLETLEPTONS AT THE LHC

The production channels of the heavy quintuplet leptonsin proton-proton collisions are dominated by the quark-antiquark annihilation via neutral and charged gaugebosons

qþ �q ! A ! �þ ��; A ¼ �; Z;W�;

where the gauge Lagrangian relevant for the production isgiven by

L � ��gauge ¼ þeð2�þþ���þþ þ �þ���þÞA�

þ g cos�Wð2�þþ���þþ þ �þ���þÞZ�

þ gð ffiffiffi2

p�þ���þþ þ ffiffiffi

3p

�0���þÞW�� þ H:c:

(23)

The cross section for the partonic process is

ðq �q ! � ��Þ ¼ ð3� 2Þ48�

sðV2L þ V2

RÞ; (24)

where s � ðpq þ p �qÞ2 is the Mandelstam variable s for the

quark-antiquark system, the parameter �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 4M2

�=sq

denotes the heavy lepton velocity, and the left- and right-handed couplings are given by

Vð�þZÞL;R ¼ Q�Qqe

2

sþ gZ�gqL;Rg

2

c2Wðs�M2ZÞ; (25)

VðW�ÞL ¼ gW�g2Vudffiffiffi

2p ðs�M2

WÞ¼ VðWþÞ�

L ; (26)

VðW�ÞR ¼ 0: (27)

Here, gqL ¼ T3 � s2WQq and gqR ¼ �s2WQq are the SM

chiral quark couplings to the Z boson. The vector couplingsof heavy leptons to gauge bosons are

gZ� ¼ T3 � s2WQ� and gW� ¼ ffiffiffi2

por

ffiffiffi3

p; (28)

where gW� can be read of the last row in Eq. (23),

relevant for the production of �þþ�þ and �þ�0 pairs,respectively.In evaluating the cross sections for a hadron collider,

the partonic cross section (24) has to be convoluted withthe appropriate parton distribution functions (PDFs). To

400 800 120010-3

10-1

101

103

400 800 1200

FIG. 4 (color online). The cross sections for production of quintuplet lepton pairs on LHC proton-proton collisions atffiffiffis

p ¼ 7 TeVvia neutral �, Z (a) and charged W� currents (b), in dependence on the heavy quintuplet mass M�.

400 800 120010-3

10-1

101

103

400 800 1200

FIG. 5 (color online). Same as Fig. 4, but for designedffiffiffis

p ¼ 14 TeV at the LHC.

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evaluate the cross sections we have used CTEQ6.6 PDFs[13] via LHAPDF software library [14].

The cross sections for proton-proton collisions arepresented on Fig. 4 for

ffiffiffis

p ¼ 7 TeV appropriate for the2011 LHC run, and for designed

ffiffiffis

p ¼ 14 TeV on Fig. 5.Thereby we distinguish separately the production via neu-tral currents shown on the left panel, and via chargedcurrents shown on the right panel of Figs. 4 and 5.

We extract in Table I the pair production cross sectionsfrom Fig. 4 for three selected values ofM�. From this tablewe find that the doubly-charged �þþ has the largest pro-duction cross section ð�þþÞjM�¼400 GeV ¼ 60:9 fb and

doubly-charged �þþ has the smallest, still comparable

ð�þþÞjM�¼400 GeV ¼ 43:5 fb. The production rates of

other heavy leptons are in between. On Fig. 6 we plot the

expected number of produced �þþ and �þþ particles forthree characteristic collider setups. In particular, for 5 fb�1

of integrated luminosity of 2011 LHC run atffiffiffis

p ¼ 7 TeV,

there should be about 520 doubly-charged �þþ or �þþ

fermions produced. In total, there should be 660 �- �� pairsproduced.

By testing the heavy lepton production cross sections,one can hope to identify the quantum numbers of thequintuplet particles, but in order to confirm their relationto neutrinos, one has to study their decays.

V. DECAYS OF QUINTUPLET STATES

Our focus here is entirely on the decay modes of theheavy lepton states listed in Eq. (7). Namely, provided thatin our scenario the exotic scalar states are slightly heavierthan the exotic leptons, the exotic scalar fields will notappear in the final states of heavy lepton decays. Note thatexotic scalar states �� ð1; 4; 1Þ were considered recentlyin [15], in the context of modified type III seesaw model.The couplings relevant for the decays at hand stem from

off-diagonal entries in the mass matrices in Eqs. (11) and(12). The diagonalization of these matrices can be achievedby making the following unitary transformations on thelepton fields:

ð�LÞc�0

R

!¼U0

ð�mLÞc�0

mR

!;

lL

ð�þR Þc

!¼UL

lmL

ð�þmRÞc

!;

lR

ð�þL Þc

!¼UR

lmR

ð�þmLÞc

!:

(29)

Following the procedure in Refs. [7,16,17], the matricesU0 and UL;R can be expressed in terms of Yv� and M.Thereby, by expanding U0 and UL;R in powers ofM�1 andkeeping only the leading-order terms, we get

U0 �V�PMNS

1ffiffi2

p v��Y

�M�1

� 1ffiffi2

p v�M�1YTV�

PMNS 1

0@

1A; (30)

UL � 1 �ffiffi3

p2 v�YM

�1ffiffi3

p2 v�M

�1Yy 1

0@

1A; UR � 1 0

0 1

!:

(31)

Here, VPMNS is a 3� 3 unitary matrix which diagonalizesthe effective light neutrino mass matrix in Eq. (21), and thenondiagonal entries are related to the sought couplings ofheavy and light leptons, and are expressed in terms of thematrix-valued quantity

Vl� ¼ ðv�YM�1Þl�: (32)

Next, for simplicity, we suppress the indices indicatingthe mass-eigenstate fields. The Lagrangian in the mass-eigenstate basis, relevant for the decays of the heavyleptons, has the neutral current part

LNCZ ¼ g

cW

���

�1

2ffiffiffi2

p VyPMNSV�

�PL

� 1

2ffiffiffi2

p VTPMNSV

���PR

��0

þ �lc� ffiffiffi

3p4

V���PR

��þ þ H:c:

�Z0�; (33)

and the charged current part

400 800 1200

101

103

105

FIG. 6 (color online). Number of �þþ and �þþ particlesproduced for three characteristic LHC collider setups, in depen-dence on the heavy lepton mass M�.

TABLE I. Production cross sections for �- �� pairs for the LHCrun at

ffiffiffis

p ¼ 7 TeV, for three selected values of M�.

Produced

pair

Cross section (fb)

M� ¼ 200 GeV M� ¼ 400 GeV M� ¼ 800 GeV

�þþ�þþ 924 34.4 0.43

�þ�þ 231 8.6 0.11

�þþ�þ 641 26.5 0.32

�þ�0 961 39.8 0.49

�þ�þþ 276 9.1 0.10

�0�þ 414 13.6 0.15

Total 3447 132 1.6

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LCC ¼ g

���

��

ffiffiffi3

2

sVyPMNSV�

�PL

þ� ffiffiffi3

p

2ffiffiffi2

p VTPMNSV

���PR

��þ þ �lð�V��PLÞ�0

þ �lc� ffiffiffi

3

2

sV���PR

��þþ

�W�

� þ H:c: (34)

Let us start our list of the partial decay widths by thedecays of neutral �0 state

�ð�0 ! ‘W�Þ ¼ g2

32�jV‘�j2

M3�

M2W

�1�M2

W

M2�

�2

��1þ 2

M2W

M2�

�;

X3m¼1

�ð�0 ! �mZ0Þ ¼ g2

32�c2W

X‘¼fe;�;�g

1

4jV‘�j2

M3�

M2Z

��1� M2

Z

M2�

�2�1þ 2

M2Z

M2�

�: (35)

The positive singly-charged heavy lepton �þ has the fol-lowing partial decay widths:

�ð�þ ! ‘þZ0Þ ¼ g2

32�c2W

3

16jV‘�j2

M3�

M2Z

�1� M2

Z

M2�

�2

��1þ 2

M2Z

M2�

�;

X3m¼1

�ð�þ ! �mWþÞ ¼ g2

32�

X‘¼fe;�;�g

15

8jV‘�j2

M3�

M2W

��1�M2

W

M2�

�2�1þ 2

M2W

M2�

�: (36)

Finally, the doubly-charged �þþ state decays exclusivelyvia a charged current, with the partial decay width

�ð�þþ ! ‘þWþÞ ¼ g2

32�

3

2jV‘�j2

M3�

M2W

�1�M2

W

M2�

�2

��1þ 2

M2W

M2�

�: (37)

The mass difference induced by loops of SM gaugebosons between two components of � quintuplet withelectric charges Q and Q0 is explicitly calculated in [1]

MQ �MQ0 ¼ �2M

4�

�ðQ2 �Q02Þs2Wf

�MZ

M

�þ ðQ�Q0Þ

� ðQþQ0 � YÞ�f

�MW

M

�� f

�MZ

M

���;

fðrÞ ¼ r

2

�2r3 lnr� 2rþ ðr2 � 4Þ1=2ðr2 þ 2Þ

� ln

�r2 � 2� r

ffiffiffiffiffiffiffiffiffiffiffiffiffiffir2 � 4

p

2

��: (38)

The values for the mass splittings �Mij ¼ Mi �Mj in

Eq. (38) for M� ¼ 400 GeV are

�M21 � M�þþ �M�þ ’ 490 MeV;

�M10 � M�þ �M�0 ’ 163 MeV;(39)

which opens additional decay channels, like �þþ !�þ�þ and �þ ! �þ�0. The decay rate for a singlepion final state is given by

400 800 120010

-1

101

103

105

10-1

10-3

10-5

FIG. 7 (color online). Partial decay widths of �0 quintupletlepton for jVl�j ¼ 3:5� 10�7, in dependence on heavy quin-tuplet mass M�.

400 800 120010-1

101

103

105

10-1

10-3

10-5

FIG. 8 (color online). Partial decay widths of �þ quintupletlepton for jVl�j ¼ 3:5� 10�7, in dependence on heavy quin-tuplet mass M�.

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�ð�i ! �j�þÞ ¼ ðgW�Þ2ij2

�G2

FjVudj2f2�ð�MijÞ3

�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� m2

�

ð�MijÞ2vuut ; (40)

where ðgW�Þ2ij is given in Eq. (28). These decays are sup-

pressed by small mass differences.In Figs. 7–9 we plot the partial widths of the decays of

�0, �þ and �þþ given in Eqs. (35)–(37), respectively.Figures 8 and 9 also show pion final state decays fromEq. (40). We list the representative final states of thesedecays in Table II, which includes same-sign dileptonevents as distinguished signatures at the LHC.

VI. POSSIBLE ROLE AS DARK MATTER

The fermionic quintuplet of this paper was selectedpreviously as a viable MDM candidate in [1]. To employit as a seesaw mediator requires additional scalar multip-lets, which makes the neutral component of the quintupletunstable. If we employ a Z2 symmetry under which� ! ��, � ! �� and all SM fields are unchanged,

the lightest component of the � and � multiplets is againa DM candidate. The quartic �5 term in the scalar potentialis still allowed so that neutrinos acquire radiatively gen-erated masses given by Eq. (17).If �0 is the DM particle, its mass is fixed by the relic

abundance to the value M� 10 TeV in [1]. The choice�5 ¼ 10�7 gives enough suppression to have small neu-trino masses with large Yukawas, Y � 0:1. In this part ofthe parameter space the model could have interestinglepton flavor violating effects like in [8].The neutral component of the scalar multiplet � could

also be a DM particle, despite its tree-level coupling to theZ boson. Similar to the inert doublet model, the �5 term inthe scalar potential in Eq. (4) splits the real and imaginaryparts of the �0 field. If the mass splitting is large enough,the inelastic scattering through the Z boson exchange iskinematically forbidden in direct detection experiments. Inthis case the new states could be within reach of the LHC.To ensure a large enough mass splitting, the coupling �5

cannot be too small. Accordingly, from Eq. (17), it followsthat the Yukawa couplings have to be smaller, suppressingthe lepton flavor violating effects.

VII. CONCLUSION

In this account we propose a TeV-scale model for neu-trino masses based only on the gauge symmetry and therenormalizability of the SM. The model employs fermionquintuplets with zero hypercharge, which in isolation cor-respond to cosmological minimal dark matter candidate.Such TeV-scale fermions in conjunction with the scalarquadruplet can generate neutrino masses both by the tree-level contributions in Fig. 1 and the loop-level contributionsin Fig. 2. Also, such states are expected to be abundantlyproduced at the LHC, and the distinctive signatures couldcome from doubly-charged components of the fermionicquintuplets. For 5 fb�1 of already accumulated integratedluminosity at the LHC (

ffiffiffis

p ¼ 7 TeV), there could be�500

produced doubly-charged�þþ or�þþ fermions, with massM� ¼ 400 GeV. The decays of these states to SM charged

400 800 120010-1

101

103

105

10-1

10-3

10-5

FIG. 9 (color online). Partial decay widths of �þþ quintupletlepton for jVl�j ¼ 3:5� 10�7, in dependence on heavy quin-tuplet mass M�.

TABLE II. Decays of exotic leptons to SM charged leptons, including multilepton and same-sign dilepton events, together with their branching ratios (restricted to l ¼ e, �) and for M� ¼400 GeV.

�þþ ! ‘�W� �þ ! ‘�Z0 �0 ! ‘þW� �0 ! ‘�Wþ(0.66) (0.06) (0.30) (0.30)

�þþ ! ‘þWþ ‘þ‘�WþW� ‘þ‘�WþZ0 � � � � � �(0.66) (0.44) (0.04) � � � � � ��þ ! ‘þZ0 ‘þ‘�Z0W� ‘þ‘�Z0Z0 ‘þ‘þZ0W� ‘þ‘�Z0Wþ(0.06) (0.04) (0.004) (0.02) (0.02)

�0 ! ‘�Wþ � � � ‘�‘�WþZ0 � � � � � �(0.30) � � � (0.02) � � � � � ��0 ! ‘þW� � � � ‘þ‘�W�Z0 � � � � � �(0.30) � � � (0.02) � � � � � �

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leptons have an interesting multilepton signature. There are,in addition, same-sign dilepton events displayed in Table II.These events have a negligible SM background, as demon-strated [18,19] in generic new physics scenario with leptonnumber violation. In particular, the detailed studies of fer-mionic triplets from type III seesaw scenario [17,20] applyto our case of fermionic quintuplets. The multilepton eventslisted in our Table II are in direct correspondence with theitems from the type III seesaw given in Table 13 of Ref. [20],to which also the analysis in [17] refers. The signals that aregood for the discovery correspond to a relatively high signalrate and small SM background, which is calculated byMADGRAPH [21]. In order to compare the signal and SM

background cross sections, we assume a particular choice ofparameters leading to the branching ratios given in Table II,restricted to l ¼ e, � leptons in the final states. In thisrespect we distinguish four classes of events containing�þ decaying to eþ or �þ lepton and Z0 ! ð‘þ‘�; q �qÞresonance to help in �þ identification:

ðiÞpp ! �þ�þ ! ð‘þZ0Þð‘�Z0Þ;which has too small of a cross section (0.03 fb with respectto the SM background of 0.6 fb) at 7 TeV LHC;

ðiiÞpp ! �þ�0 ! ð‘þZ0Þð‘�WþÞ;which has a cross section of 0.7 fb, comparable to the SMbackground of 0.8 fb;

ðiiiÞpp ! �þ�0 ! ð‘þZ0Þð‘þW�Þ;the LNV event having 0.7 fb with the same-sign dileptonstate, which is nonexistent in the SM and thus devoid of theSM background;

ðivÞpp ! �þþ�þ ! ð‘þWþÞð‘�Z0Þ;

having a relatively high signal rate (1.1 fb with respect tothe SM background of 0.8 fb). The classes (iii) and (iv) leadto signals elaborately detailed in [17,20], which can berescaled to infer on the LHC discovery reach.The model of neutrino mass generation presented

here represents a generalization of the fermion tripletseesaw mediator from the type III seesaw model to ahypercharge-zero quintuplet, which we postponed at thetime of elaborating first its nonzero hypercharge variantin [6]. The hypercharge-zero quintuplet has been proposedsubsequently in [22]. One can question the possibilityto distinguish between the present hypercharge-zeroquintuplet with a doubly-charged component and pre-viously considered nonzero hypercharge states [6,7],which provide spectacular falsifiable triply-charged sig-natures. Consequently, a nonobservation of the latterwould put in a forefront the hypercharge-zero quintu-plets, which provide their neutral components as poten-tial MDM candidates. However, a blow to the stabilityof such DM comes from the presence of additionalfields needed to generate the described small neutrinomasses. As usual, the stability can be restored by in-troducing the discrete symmetry under which the newstates are odd, in which case neutrinos get mass onlyfrom radiative contributions.

ACKNOWLEDGMENTS

This work is supported by the Croatian Ministry ofScience, Education, and Sports under Contract No. 119-0982930-1016.

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